Hardy-Lieb-Thirring inequalities for eigenvalues of Schrödinger operators
2007 (English)Doctoral thesis, comprehensive summary (Other scientific)
This thesis is devoted to quantitative questions about the discrete spectrum of Schrödinger-type operators.
In Paper I we show that the Lieb-Thirring inequalities on moments of negative eigen¬values remain true, with possibly different constants, when the critical Hardy weight is subtracted from the Laplace operator.
In Paper II we prove that the one-dimensional analog of this inequality holds even for the critical value of the moment parameter. In Paper III we establish Hardy-Lieb-Thirring inequalities for fractional powers of the Laplace operator and, in particular, relativistic Schrödinger operators. We do so by first establishing Hardy-Sobolev inequalities for such operators. We also allow for the inclu¬sion of magnetic fields.
As an application, in Paper IV we give a proof of stability of relativistic matter with magnetic fields up to the critical value of the nuclear charge.
In Paper V we derive inequalities for moments of the real part and the modulus of the eigen¬values of Schrödinger operators with complex-valued potentials.
Place, publisher, year, edition, pages
Stockholm: KTH , 2007. , vii, 28 p.
Trita-MAT. MA, ISSN 1401-2278 ; 07:03
IdentifiersURN: urn:nbn:se:kth:diva-4344ISBN: 978-91-7178-626-5OAI: oai:DiVA.org:kth-4344DiVA: diva2:11908
2007-05-09, Sal F3, KTH, Lindstedtsvägen 26, Stockholm, 09:00
Solovej, Jan Philip, Professor
QC 201007082007-04-252007-04-252010-07-08Bibliographically approved
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